DS6 (now in 3rd) did a mid-year skip from K to 1st. Since his K was half-day, we began the transition by having him go to K in the morning, eat lunch with me, and then go to 1st in the afternoon for the first week. The second week, he still did K in the morning, but then ate lunch with his new class. All went smoothly and he was fully transitioned to 1st after 3 weeks.
The kids were told that the principal decided to move DS to a different class. It's a large school, and there is a high turnover anyway, so that did not seem strange. We de-emphasized the change in grade level, and made sure to place the authority for the decision with the principal so that it would not seem that this was simply done at parental request.
DS just began doing the 1st grade work with his new class. There was no catching up. Since they don't allow skips unless the child is two grade levels ahead, that was not a problem.
He is still able to play with the kids he knew in K at recess, and is in the same cub scout den with some of those boys. So he still has contact with them.
